Answer:
- x=7
- ∠GBD=112
- ∠EFC=112
Step-by-step explanation:
Here, we need to know about the concept of the alternate interior angle theorem. This says that the alternate interior angle of two parallel lines formed with one transversal is equal. For a more graphical explanation, please refer to the attachment below.
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Given
∠GBD=4x+84
∠EFC=16x
m∠GBD=m∠EFC
Solve
4x+84=16x ⇔ Given
4x+84-4x=16x-4x ⇔ Subtract 4x on both sides
84=12x ⇔ Simplify
84/12=12x/12 ⇔ Divide 12 on both sides
x=7 ⇔ Simplify
Substitute the x value into each angle expression
∠GBD=4x+84=4(7)+84=28+84=112
∠EFC=16x=16(7)=112
Hope this helps!! :)
Please let me know if you have any questions
